It's easy to speculate about Contact and the future, and lots of folks have. However incorrect it turns out to be in hindsight, it can still be useful in promoting thought and discussion of 'knowns, known unknowns, and unknown unknowns'.
There several critical decisions for the ETs regarding how to proceed with contact.
1) Should they provide a summary of information, and offer to provide more details on request; or a large package of information--enough to convey as much as possible of the information they consider critical, but small enough to be made available on the Internet?
2) Should they (initially) include information about religions of other civilizations similar to ours; and their (ETs') knowledge of metaphysics?
3) Should they (initially) provide information on science and technology, especially energy technology?
4) Should they (initially) tell us the whole story of their role in our history?
Without their knowledge--especially of past Contact experiences--we can't know what choices they would make.
What would we learn if they provided access to most of what they know? Most, if not all of the following is known by various people, and presumably already known by elements of all major governments.
>Critical Failure Modes
Existing critical vulnerabilities and risks (e.g., large nuclear arsenals, the vulnerability of the cybernetic and electrical grids to solar EMP and hacking; pandemics, etc.) will increase dramatically with the rapid evolution of genetic engineering, synthetic life, nanotechnology, and Artificial Intelligence, etc., and increases in drug resistant microbes, massive species extermination (extinction), Global Warming, and the continuing environmental degradation of the Earth, etc.
>The End of Life As We Have Known It For A Very Long Time
In the 'worst' case, from the ETs' perspective, while not 'technically' inevitable, as a practical matter--due to our attitudes, political realities, rapidly evolving technologies, technological and environmental vulnerabilities, etc.--a major collapse and even depopulation in the next few decades of some or perhaps many technologically advanced as well as developing nations may be likely.
Absent such a collapse, in many critical respects, life as we've known it for millennia is coming to an end anyhow--as a result of the rapidly evolving technologies mentioned above.
>Consciousness, Reality, and Spirituality
Contact will begin a revolution in the science of metaphysics--the study of consciousness, reality, and spirituality, and human health and well being. Necessarily, this will end the theology of reductionist materialism; and will be the beginning of a slow end for elaborate 'divine-authority' religious theologies, except as cultural traditions and refuges for a few 'true believers'.
'Psychic phenomena' are absolutely real, but at present, human psychic abilities--except for healing others--are rarely significant in our reality. There's nothing inherently good or evil about psychic abilities, since everyone is 'psychic', and every day their thoughts, etc., influence themselves and other people, and the world--for better or worse--whether they know it or not, and for most people, whether they like it or not.
Something like the LOA ('Law of Attraction'), combined with something like EFT ('Emotional Freedom Technique', etc.) will be of immensely greater importance than any efforts to increase our 'psychic' powers, and science will explore the continuum of these two related understandings of the relationship between consciousness and reality, and the ability of humans to construct the realities we experience, and in particular the equations which characterize intentions, etc., and relate intentions, etc., time, and consequences...and the nature of the interaction between and among individual and collective consciousnesses, and whether the intentions of a group of people, synchronized or 'harmonized' by some means, can significantly affect the reality experienced by the group.
The understanding that humans have remarkable abilities to heal themselves, emotionally and physically, will have enormous consequences for our civilization. For most people, in most cases, this power can be significantly increased by the interaction with one or more healers. From the perspective of current medical knowledge, this might be understood as an extraordinary and deliberate enhancement of the 'placebo effect'.
Perhaps the most critical question for science is: are the "Laws of Physics" as we believe we know them, absolute, or only our constructions, overlaid on some deeper truths and realities?
While scientific and technological knowledge the ETs could provide might be critical, by far the most important scientific issue is metaphysics, and a change in the consciousness of humankind--a spiritual revolution. Even a new energy source, or an extraordinary new understanding of our planetary environment, etc., while they might be critical to our survival, will not ensure our survival unless our attitudes change.
Wild, or not, speculation: there is no 'objective' past, present, or future. All exist simultaneously, and there are probabilistic preferences, i.e., 'lowest energy solutions', but all are changed 'simultaneously' by conscious choices and intentions.